Simplify the following expression: $ q = \dfrac{7}{8} - \dfrac{-7}{k + 2} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k + 2}{k + 2}$ $ \dfrac{7}{8} \times \dfrac{k + 2}{k + 2} = \dfrac{7k + 14}{8k + 16} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-7}{k + 2} \times \dfrac{8}{8} = \dfrac{-56}{8k + 16} $ Therefore $ q = \dfrac{7k + 14}{8k + 16} - \dfrac{-56}{8k + 16} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{7k + 14 + 56 }{8k + 16} $ Distribute the negative sign: $q = \dfrac{7k + 14 + 56}{8k + 16}$ $q = \dfrac{7k + 70}{8k + 16}$